An underwater vehicle pulsating flow field equivalent model simulation method and device
By combining empirical formula prediction and steady-state correction grid generation methods with large eddy simulation, the problem of simulating pulsating flow of underwater vehicles at high Reynolds numbers was solved, achieving efficient prediction of flow physical quantities, especially accurate simulation of wall pressure pulsation, and reducing computational resource consumption.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2023-10-25
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies struggle to accurately simulate the pulsating flow of underwater vehicles at high Reynolds numbers, especially the wall pressure pulsation phenomenon within the boundary layer. Furthermore, traditional methods consume excessive computational resources, making them unsuitable for practical engineering needs.
A grid generation method based on empirical formula prediction and steady calculation correction is adopted. Combined with the large eddy simulation method that considers turbulent anisotropy and unsteady effects in the inner boundary layer, a CFD solver is constructed. By dynamically adjusting the model coefficients, accurate calculation of subgrid stress is achieved. Furthermore, an unsteady wall stress model with pressure gradient effects is introduced to reduce the number of grids and improve computational efficiency.
By reducing the grid size to 10⁷, the system accurately simulates the pulsating flow of underwater vehicles, predicts wall pressure pulsations, improves computational efficiency, and reduces computational resource consumption.
Smart Images
Figure CN117371353B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of underwater vehicle technology, specifically to a simulation method and apparatus for an equivalent model of pulsating flow field of an underwater vehicle. Background Technology
[0002] Numerical simulation of underwater vehicle flow is closely related to practical engineering problems such as hydrodynamic optimization, structural flow-induced noise, and hydrodynamic noise. However, in actual operating conditions, the Reynolds number of underwater vehicle flow can reach as high as 10⁷-10⁹, and is often accompanied by complex physical phenomena such as laminar-turbulent transition and flow separation. To address this, the Reynolds-averaged simulation (RANS) method commonly used in industry can only predict overall physical quantities such as hydrodynamics, and is difficult to handle flow field fluctuations and provide detailed flow structures. However, using the traditional large eddy simulation method requires a large number of meshes near the surface of the underwater vehicle to correctly solve the flow within the boundary layer, consuming more than 90% of the total computational resources. (The text then continues with a discussion of Reynolds number 10⁷-10⁹.) 6 Taking the large eddy simulation of underwater vehicles of this magnitude as an example, the computational grid used reached an astonishing 10^10. 9 The magnitude of this makes it difficult to apply in practical engineering problems. In recent years, the separated eddy simulation (DES) method has become a popular numerical simulation method for handling high Reynolds number flows. Its basic idea is to use the RANS method to solve the problem in the boundary layer region and the LES method to solve the problem outside the boundary layer. However, because this method still uses the RANS method to solve the problem inside the boundary layer, it is difficult to accurately obtain the pulsating physical quantities within the boundary layer, and it cannot meet the requirements of the wall pressure pulsation phenomenon that is of great concern in practical engineering problems.
[0003] On the other hand, traditional subgrid models are mainly designed for isotropic turbulence, based on the assumption of local equilibrium where energy production and dissipation offset each other. The coefficients in the model are usually constant values selected empirically. However, since the flow field is dynamically changing, and the subgrid viscosity ν near the wall varies... sgs The corresponding decrease is due to the fact that traditional subgrid models often produce excessive dissipation during calculations, making them unsuitable for near-wall and free shear flows. Furthermore, because they do not consider energy transfer processes, they cannot reflect the properties of local energy transport or the reverse energy transfer effect within the flow. Summary of the Invention
[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method and apparatus for simulating the equivalent model of the pulsating flow field of an underwater vehicle that can predict the pulsating flow field while meeting practical engineering requirements.
[0005] To solve the above problems, the technical solution of the present invention is as follows:
[0006] A simulation method for an equivalent model of the pulsating flow field of an underwater vehicle includes the following steps:
[0007] For underwater vehicles, a computational grid is generated using empirical formulas for prediction and steady-state calculation correction.
[0008] A CFD solver is constructed based on the large eddy simulation method that considers turbulent anisotropy and unsteady effects in the inner boundary layer.
[0009] Based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation, the physical quantities on the surface of the underwater vehicle and in the pulsating flow field are solved.
[0010] Preferably, the step of generating a computational grid for underwater vehicles using empirical formulas for prediction and steady-state calculation correction specifically includes:
[0011] Predict the boundary layer thickness at the end of the parallel midbody section of an underwater vehicle based on an empirical formula for flat plate boundary layer thickness: Where x is the current-direction distance from the bow of the underwater vehicle, Re x The direction Reynolds number is obtained based on x and the incoming flow velocity;
[0012] After estimating the boundary layer thickness, the height of the first layer mesh near the wall is set to: Δy w =1 / 50δ, a total of 30 grid layers are set, the extension ratio is 1.03, and the ratio of the grid size in the flow direction and span direction to the height of the first grid layer near the wall does not exceed 10;
[0013] After the computational grid is drawn, the flow field is solved using the steady RANS method. After the solution converges, the velocity profile at the end of the parallel midbody section of the underwater vehicle is output, and the actual boundary layer thickness is determined according to 99% of the incoming flow velocity.
[0014] The computational grid is modified based on the actual boundary layer thickness to obtain a computational grid that meets the requirements.
[0015] Preferably, the step of constructing a CFD solver based on a large eddy simulation method that considers turbulent anisotropy and unsteady effects in the inner boundary layer specifically includes: employing the single-phase incompressible Navier-Stokes equations in the solver, including the continuity equation and the momentum equation:
[0016]
[0017]
[0018]
[0019] in, It is the filtered speed. The pressure is the filtered value, ρ is the density, ν is the molecular kinematic viscosity, and τ is the molecular viscosity. sgs It is the sublattice stress tensor, ν sgs It is subgrid viscosity. It is the strain tensor; in order to solve for ν sgs The transport equations obtained by employing a dynamic k-equation subgrid model considering turbulent anisotropy are as follows:
[0020]
[0021]
[0022] Where, k sgs For subgrid kinetic energy, Δ is the filtering scale, determined by the grid scale; C k and C ε For the dynamic k-equation subgrid model, these are all functions of time and space, dynamically adjusted according to the flow field state to adapt to the dynamically changing flow field.
[0023] Preferably, the step of constructing a CFD solver based on the large eddy simulation method considering turbulent anisotropy and unsteady effects in the inner boundary layer specifically includes: introducing a wall stress model including time derivative and pressure gradient terms; sampling at a specified distance h from the wall; inputting the sampled flow physical quantities such as velocity, velocity gradient, pressure gradient, and time derivative into the wall stress model to calculate the wall shear stress; and finally applying it to the corresponding wall location; using a non-equilibrium wall stress model considering unsteady and pressure gradient effects, derived from the thin boundary layer equations.
[0024]
[0025] Where i = 1, 3 represent directions parallel to the wall, ν t The viscosity is turbulent; in the CFD solver, this wall stress model is embedded as a turbulent viscosity boundary condition, as shown in the formula:
[0026]
[0027]
[0028] Preferably, the step of solving for the physical quantities on the surface of the underwater vehicle and in the fluctuating flow field based on the equivalent model parameters recommended in the numerical simulation and the applicable boundary conditions and initial conditions specifically includes: when setting the initial conditions for unsteady LES calculation, the converged pressure and velocity fields are calculated using the steady RANS method as the initial fields, thereby reducing the calculation time required to achieve flow stability; when setting the boundary conditions for unsteady LES calculation, the inlet of the computational domain is set as a steady incoming flow, the outlet of the computational domain is set as a zero gradient boundary condition, the perimeter of the computational domain is set as a symmetric boundary condition, and the surface of the underwater vehicle is set as a no-slip boundary condition.
[0029] Preferably, the step of solving for the physical quantities on the surface of the underwater vehicle and in the pulsating flow field based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation specifically includes: solving for the physical quantities on the surface of the underwater vehicle and in the pulsating flow field by solving the governing equations through a PISO loop based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation.
[0030] Furthermore, the present invention also provides a simulation apparatus for an equivalent model of a pulsating flow field of an underwater vehicle, comprising a processor and a memory for storing executable instructions of the processor, the processor being configured to execute the simulation method for an equivalent model of a pulsating flow field of an underwater vehicle as described above by executing the executable instructions.
[0031] Compared with the prior art, the advantages of the present invention are as follows:
[0032] 1. Compared with the traditional mesh generation method that only considers the first layer of mesh near the wall, this invention proposes a mesh generation method based on empirical formula prediction and steady RANS calculation correction, and gives recommended parameters for boundary layer mesh.
[0033] 2. By adopting a dynamic subgrid model that considers the anisotropy of turbulence, reverse energy transfer from small eddies to large eddies at the subgrid scale can be realized, and the model coefficients can be adjusted in real time according to local flow information, thus ensuring the accurate calculation of subgrid stress.
[0034] 3. This invention can reduce the grid size from 10 to 10 when simulating the flow of an underwater vehicle. 9 Reduced to 10 7 This greatly improves computational efficiency. Attached Figure Description
[0035] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:
[0036] Figure 1This is a flowchart of the simulation method for the equivalent model of the pulsating flow field of an underwater vehicle according to the present invention;
[0037] Figure 2 This is a detailed flowchart of the simulation method for the equivalent model of the pulsating flow field of an underwater vehicle according to the present invention;
[0038] Figure 3 The flowchart shows the calculation process of the wall stress model considering unsteady and pressure gradient effects in this invention.
[0039] Figure 4 The flowchart shows the calculation process of the subgrid model considering turbulent anisotropy in this invention.
[0040] Figure 5 This is a schematic diagram of a SUBOFF standard model according to a specific embodiment of the present invention;
[0041] Figure 6 This is a schematic diagram of the computational domain of the SUBOFF standard model according to a specific embodiment of the present invention;
[0042] Figure 7 This is a schematic diagram of the near-wall computational mesh of a SUBOFF standard model according to a specific embodiment of the present invention;
[0043] Figure 8 This is a curve of the average surface pressure coefficient of an underwater vehicle obtained by SUBOFF standard model calculation in a specific embodiment of the present invention;
[0044] Figure 9 This is a curve of the average surface friction coefficient of an underwater vehicle surface obtained by SUBOFF standard model calculation in a specific embodiment of the present invention;
[0045] Figure 10 This is a dimensionless variance plot of the wake pulsating velocity at x / D=3 obtained by SUBOFF standard model calculation in a specific embodiment of the present invention;
[0046] Figure 11 This is a schematic diagram of the pressure measuring points on a SUBOFF standard model according to a specific embodiment of the present invention;
[0047] Figure 12 This is a time-history curve of each pressure measuring point obtained by SUBOFF standard model calculation in a specific embodiment of the present invention. Detailed Implementation
[0048] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.
[0049] Specifically, this invention provides a simulation method for an equivalent model of the pulsating flow field of an underwater vehicle, such as... Figure 1 and Figure 2 As shown, the method includes the following steps:
[0050] S1: For underwater vehicles, the computational grid is generated by using empirical formulas for prediction and steady-state calculation correction.
[0051] Specifically, when drawing the computational grid for an underwater vehicle, the following steps are included:
[0052] First, the boundary layer thickness at the end of the parallel midbody section of the underwater vehicle is estimated using an empirical formula for the boundary layer thickness of a flat plate:
[0053]
[0054] Where x is the current-direction distance from the bow of the underwater vehicle, Re x The flow-direction Reynolds number is obtained based on x and the incoming flow velocity. After estimating the boundary layer thickness, the height of the first mesh layer near the wall is set to Δy. w =1 / 50δ, a total of 30 mesh layers were set, with an extension ratio of 1.03. The ratio of the mesh scale in the flow direction and spanwise direction to the height of the first mesh layer near the wall did not exceed 10. After the computational mesh was drawn, the flow field was solved using the steady RANS method. After the solution converged, the velocity profile at the end of the parallel midbody section of the underwater vehicle was output, and the actual boundary layer thickness was determined based on 99% of the incoming flow velocity. Finally, based on the actual boundary layer thickness, the computational mesh was corrected according to the above requirements to obtain a final computational mesh that meets the requirements.
[0055] S2: Construct a CFD solver based on the large eddy simulation method that considers turbulent anisotropy and unsteady effects in the inner boundary layer;
[0056] Specifically, for CFD solvers that consider turbulent anisotropy and unsteady effects within the boundary layer in large eddy simulation methods, the following are included:
[0057] The solver employs the single-phase incompressible Navier-Stokes equations, including the continuity equation and the momentum equation.
[0058]
[0059]
[0060]
[0061] in, It is the filtered speed. The pressure is the filtered value, ρ is the density, ν is the molecular kinematic viscosity, and τ is the molecular viscosity.sgs It is the sublattice stress tensor, ν sgs It is subgrid viscosity. It is the strain tensor.
[0062] In order to obtain ν sgs The transport equations obtained by using a dynamic k-equation subgrid model that considers turbulent anisotropy are shown below:
[0063]
[0064]
[0065] Where, k sgs C represents the subgrid kinetic energy, where Δ is the filtering scale, determined by the grid scale. k and C ε For the dynamic k-equation subgrid model, these are model coefficients, functions of time and space, dynamically adjusted according to the flow field state to adapt to the dynamically changing flow field. In the CFD solver, the computational flow for the dynamic subgrid model considering turbulent anisotropy is as follows: Figure 3 As shown.
[0066] Building upon the above, to further consider the unsteady effects of the inner boundary layer under complex actual conditions such as acceleration and deceleration, a wall stress model including time derivative and pressure gradient terms is introduced. The basic idea is to sample at a specified distance h from the wall, and input the obtained flow physical quantities such as velocity, velocity gradient, pressure gradient, and time derivative into the wall stress model to calculate the wall shear stress, which is then applied to the corresponding wall location. In this invention, a non-equilibrium wall stress model considering unsteady and pressure gradient effects is used, derived from the thin boundary layer equation.
[0067]
[0068] Where i = 1, 3 represent directions parallel to the wall, ν t Let be the turbulent viscosity. In the wall stress model considered in this invention, the right-hand side of the equation retains the time derivative term representing the unsteady effect and the pressure gradient term representing the pressure gradient effect, respectively. In the CFD solver, this wall stress model is embedded in the form of turbulent viscosity boundary conditions, as shown in the following equation:
[0069]
[0070]
[0071] In a CFD solver, the calculation process for a wall stress model considering unsteady effects and pressure gradient effects is as follows: Figure 4 As shown.
[0072] S3: Based on the equivalent model parameters recommended in the numerical simulation and the applicable boundary and initial conditions, solve for the physical quantities on the surface of the underwater vehicle and in the pulsating flow field.
[0073] Specifically, in setting the recommended equivalent model parameters, applicable boundary conditions, and initial conditions for the numerical simulation, the sampling height h is set to 1 / 20δ from the wall. When setting the initial conditions for the unsteady LES calculation, the converged pressure and velocity fields obtained using the steady RANS method are used as the initial fields to reduce the computation time required to achieve flow stability. When setting the boundary conditions for the unsteady LES calculation, the inlet of the computational domain is set to a steady inflow, the outlet to a zero-gradient boundary condition, the perimeter of the computational domain to symmetric boundary conditions, and the surface of the underwater vehicle to a no-slip boundary condition. Based on the recommended equivalent model parameters, applicable boundary conditions, and initial conditions given in the numerical simulation, the physical quantities on the surface of the underwater vehicle and in the fluctuating flow field are obtained by solving the governing equations using a PISO loop.
[0074] Simulation results verification:
[0075] This invention provides a specific embodiment for numerical calculations under high Reynolds number conditions based on the SUBOFF standard model. A schematic diagram of the SUBOFF standard model used in this embodiment is shown below. Figure 5 As shown, the diameter D of the parallel central body is 0.508m, and the total length L is 8.6D = 4.356m. The schematic diagram of the computational domain used in this embodiment is shown below. Figure 6 As shown, the computational domain inlet is 10 times the diameter from the bow of the underwater vehicle, the computational domain outlet is 30 times the diameter from the stern, and the perimeter of the computational domain is 10 times the diameter from the centerline of the underwater vehicle. A schematic diagram of the near-wall computational mesh used in this embodiment is shown below. Figure 7 As shown, 30 mesh layers are arranged within the boundary layer thickness δ, with a growth rate of 1.03. The height Δyw of the first mesh layer near the wall is 1 / 50δ, and the flow and circumferential mesh sizes are Δx=Δz=1 / 10δ, with a total mesh count of 2.2×10⁷. In the wall stress model settings, the sampling height h is set at the center of the third mesh layer near the wall, corresponding to 1 / 20δ.
[0076] To verify the accuracy of this invention, the calculated results were first compared with publicly available experimental data. The definitions of the pressure coefficient and the surface friction coefficient are as follows:
[0077]
[0078]
[0079] Among them, U ∞ p is the incoming flow velocity.∞ For the pressure at infinity, τ w This represents the wall shear stress. Figure 8 and Figure 9 The curves showing the average pressure coefficient and average surface friction coefficient of the underwater vehicle surface are presented respectively. It can be seen from these curves that the present invention can accurately predict the average flow physical quantities of underwater vehicles. Figure 10 The dimensionless variance of the flow-direction pulsating velocity at x / D = 3 in the wake of the underwater vehicle is further demonstrated, where U x ′ represents the flow pulsation velocity, U e The value represents the edge velocity at this cross-section. Comparison reveals that the calculated results obtained by this invention agree well with experimental data, further demonstrating that this invention can be used to predict the physical quantities of pulsating flow in underwater vehicles.
[0080] Figure 11 This is a schematic diagram of six pressure measurement points set on the surface of an underwater vehicle, located at the bow, midsection, and stern, corresponding to the reverse pressure gradient, zero pressure gradient, and compressive pressure gradient regions, respectively. Figure 12 The time-history curves of various pressure measurement points on the surface of the underwater vehicle are shown. Figure 12 As can be seen from this, the present invention can predict the pressure pulsation characteristics on the surface of underwater vehicles very well.
[0081] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.
Claims
1. A simulation method for an equivalent model of the pulsating flow field of an underwater vehicle, characterized in that, The method includes the following steps: For underwater vehicles, a computational grid is generated using empirical formulas for prediction and steady-state calculation correction. Specifically, this includes: Predict the boundary layer thickness at the end of the parallel midbody section of an underwater vehicle based on an empirical formula for flat plate boundary layer thickness: ,in, The distance from the bow of the underwater vehicle in the direction of the current. According to The flow direction Reynolds number is obtained from the incoming flow velocity; After estimating the boundary layer thickness, the height of the first layer mesh near the wall is set as follows: A total of 30 grid layers were set up with an extension ratio of 1.
03. At the same time, the ratio of the grid size in the flow direction and span direction to the height of the first grid layer near the wall did not exceed 10. After the computational grid is drawn, the flow field is solved using the steady RANS method. After the solution converges, the velocity profile at the end of the parallel midbody section of the underwater vehicle is output, and the actual boundary layer thickness is determined according to 99% of the incoming flow velocity. The computational grid is modified according to the actual boundary layer thickness to obtain a computational grid that meets the requirements. A CFD solver is constructed based on the large eddy simulation method that considers turbulent anisotropy and unsteady effects in the inner boundary layer. Based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation, the physical quantities on the surface of the underwater vehicle and in the pulsating flow field are solved.
2. The simulation method for the equivalent model of the pulsating flow field of an underwater vehicle according to claim 1, characterized in that, The steps for constructing a CFD solver based on the large eddy simulation method considering turbulent anisotropy and unsteady effects in the inner boundary layer specifically include: employing the single-phase incompressible Navier-Stokes equations in the solver, including the continuity equation and the momentum equation: in, It is the filtered speed. It is the filtered pressure. It's density. It is the viscosity of molecular motion. It is the sublattice stress tensor. It is subgrid viscosity. It is the strain tensor; in order to solve for it... The transport equations obtained by employing a dynamic k-equation subgrid model considering turbulent anisotropy are as follows: in, For sublattice kinetic energy, It is the filtering scale, determined by the grid scale; and For the dynamic k-equation subgrid model, these are all functions of time and space, dynamically adjusted according to the flow field state to adapt to the dynamically changing flow field.
3. The simulation method for the equivalent model of the pulsating flow field of an underwater vehicle according to claim 2, characterized in that, The steps for constructing a CFD solver based on the large eddy simulation method considering turbulent anisotropy and unsteady effects in the inner boundary layer specifically include: introducing a wall stress model including time derivative and pressure gradient terms; sampling at a specified distance h from the wall; inputting the obtained flow physical quantities such as velocity, velocity gradient, pressure gradient, and time derivative into the wall stress model to calculate the wall shear stress, and finally applying it to the corresponding wall location; and using a non-equilibrium wall stress model considering unsteady and pressure gradient effects, derived from the thin boundary layer equation. in, Represents a direction parallel to the wall. The viscosity is turbulent; in the CFD solver, this wall stress model is embedded as a turbulent viscosity boundary condition, as shown in the formula: 。 4. The simulation method for the equivalent model of the pulsating flow field of an underwater vehicle according to claim 1, characterized in that, The steps for solving the physical quantities on the surface of the underwater vehicle and in the fluctuating flow field based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation specifically include: when setting the initial conditions for unsteady LES calculation, the converged pressure and velocity fields are calculated using the steady RANS method as the initial fields to reduce the computation time required to achieve flow stability; when setting the boundary conditions for unsteady LES calculation, the inlet of the computational domain is set as a steady inflow, the outlet of the computational domain is set as a zero-gradient boundary condition, the perimeter of the computational domain is set as a symmetric boundary condition, and the surface of the underwater vehicle is set as a no-slip boundary condition.
5. The simulation method for the equivalent model of the pulsating flow field of an underwater vehicle according to claim 4, characterized in that, The step of obtaining the physical quantities on the surface of the underwater vehicle and in the pulsating flow field based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation specifically includes: obtaining the physical quantities on the surface of the underwater vehicle and in the pulsating flow field by solving the governing equations through PISO loops based on the equivalent model parameters, applicable boundary conditions, and initial conditions recommended in the numerical simulation.
6. A simulation device for an equivalent model of the pulsating flow field of an underwater vehicle, characterized in that, The device includes a processor and a memory for storing executable instructions of the processor, the processor being configured to perform the underwater vehicle pulsating flow field equivalent model simulation method as described in any one of claims 1 to 5 by executing the executable instructions.